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An important aspect of the EPA/ISTA is the freedom of the aikido teachers to teach and grade the way they want. In other organisations there is a grading commision (at least for the dan-grades) that decides who passes, which means they decide what kind of aikido is to be taught (unless you don't care about rank).
Of course there are indepent dojo as well.

So my questions are:
with what kind of federation are you affiliated, if any?
how close are the ties between that federation and the main organisation of your style?
and most importantly, what are the advantages/disadvantages?

I am in a small, independent affiliating headed by a high grade and technically excellent Chief Instructor (which is run as a non-profit making organisation). The advantage is there are no politics and our focus is purely on aikido. Also, although I have immense respect for the chief instructor, I can teach the aikido that I do, whilst still exposing my students to the aikido of the chief instructor and associated instructors. i.e. I don't have to pretend to teach what the chief instructor is teaching before I have internalised and integrated that which I think is useful into my own aikido.

We are still open to train with whomever we want externally, so we don't limit our ability to learn from other instructors. I see this as the ideal situation and am very happy with it. As far as gradings go, although the teaching method is undoubteldy different from that of the chief instructor, I grade low grades myself, but occasionally ensure that we are at least meeting the same standard required by the chief instructor by occasional gradings with them.

I would hate to be in a larger organisation with all the politics and also I would hate to have my ability to question and explore aikido as an instructor heavily restricted by other authorities.

On the notion of advantage/disadvantage, it would seem to be based upon where your interests would lie. A distinction would have to be made, I feel, between federation recognition and acquired skill. One would have to ask where his/her interests lay, since it is a false assumption that one of these elements means the guaranteed presence of the other. Of course, this is not to say that one cannot become skilled inside of a federation. This is only to say that federation alignment in no way guarantees skill acquisition -- in the same way that independence does not guarantee a lack of skill. However, if federation recognition is what you are interested in, then there is only one way to get that -- join the federation.

I would say it is important to realize these differences since most federations have it as part of their overall discourse that skill can only be attained within. As part of that discourse, one should also realize that federations portray themselves as a (more or less) unified whole. Of course, anyone knows that this is hardly true, but everyone tends to use such a notion when it comes to defining themselves against some kind of Other -- be that from another federation or from an independent source.

Part of this is how federations like to portray themselves through the examination. There is this idea that huge degrees of subjectivity are NOT present -- that the examination is some sort of objective instrument through which cohesion and transmission is guaranteed and thus through which the federation is made whole and distinct. In actuality, huge degrees of subjectivity, as well as objective aspects that have nothing to do with cohesion and transmission (e.g. a given political economy), are present in the examination. This happens to such a degree that one can actually see much more variation inside of a federation than inside of a more independent system of transmission.

Hence, just because someone is of an independent system of transmission, it does not mean that he/she is subject to huge degrees of variation, where transmission becomes a fuddled mess of personal interests and priorities. In the same way, being federated does not at all mean that one will remain part of a pure system of transmission -- that one will not belong more to a fuddled mess of personal interests and priorities.

In my opinion, you are going to have to look to the person doing the transmitting, and also at the system of transmission, to determine the real advantages and disadvantages of one system over another if skill acquisition is your only interest (or the main interest you have out of many).